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A326878 Number of topologies whose points are a subset of {1..n}. 23
1, 2, 7, 45, 500, 9053, 257151, 11161244, 725343385, 69407094565, 9639771895398, 1919182252611715, 541764452276876719, 214777343584048313318, 118575323291814379721651, 90492591258634595795504697, 94844885130660856889237907260, 135738086271526574073701454370969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

Wikipedia Topological space

EXAMPLE

The a(0) = 1 through a(2) = 7 topologies:

  {{}}  {{}}      {{}}

        {{},{1}}  {{},{1}}

                  {{},{2}}

                  {{},{1,2}}

                  {{},{1},{1,2}}

                  {{},{2},{1,2}}

                  {{},{1},{2},{1,2}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n]]], MemberQ[#, {}]&&SubsetQ[#, Union[Union@@@Tuples[#, 2], Intersection@@@Tuples[#, 2]]]&]], {n, 0, 4}]

(* Second program: *)

A000798 = Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {_, _}][[All, 2]];

a[n_] := Sum[Binomial[n, k]*A000798[[k+1]], {k, 0, n}];

a /@ Range[0, Length[A000798]-1] (* Jean-Fran├žois Alcover, Dec 30 2019 *)

CROSSREFS

Binomial transform of A000798 (the covering case).

Cf. A001930, A003465, A014466, A102896, A102897, A306445, A326866, A326876.

Sequence in context: A066612 A098637 A162045 * A153549 A079491 A266908

Adjacent sequences:  A326875 A326876 A326877 * A326879 A326880 A326881

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 30 2019

STATUS

approved

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Last modified June 21 02:05 EDT 2021. Contains 345342 sequences. (Running on oeis4.)